Definition 5.18 Let \(\widehat{X}_{(1)}\)  denote the blow-up of \(X\)  along the closure of \(B^{(1)}(X)\) , with exceptional divisor denoted by \(E_{(1)}\) . As the centre of this blow-up is \(P\) -invariant, there is an induced \(P\) -action on \(\widehat{X}_{(1)}\)  which we linearise by the pulling back the linearisation on \(X\)  and perturbing by a small multiple of the exceptional divisor \(E^{1}\)  as in [1]}.

